We study an allocation problem where a set of objects needs to be allocated to agents arriving over time. The basic model is of the private, independent values type. The dynamically efficient allocation is implementable if the distribution of agents' values is known. Whereas lack of knowledge about the distribution is inconsequential in the static case, endogenous informational externalities arise if the designer gradually learns about the distribution by observing present values. These externalities may prevent the implementation of the dynamically efficient allocation. We provide necessary and sufficient conditions for the efficient allocation to be implementable.

We study two-sided markets with a finite number of agents on each side, and with two-sided incomplete information. Agents are matched assortatively on the basis of costly signals. Asymmetries in signalling activity between the two sides of the market can be explained by asymmetries either in size or in heterogeneity. Our main results identify general conditions under which the potential increase in expected output due to assortative matching (relative to random matching) is offset by the costs of signalling. Finally, we examine the limit model with a continuum of agents and point out differences and similarities to the finite version. Technically, the paper is based on the elegant theory about stochastic order relations among differences of order statistics, pioneered by Barlow and Proschan in 1966 in the framework of reliability theory.